Wikipedia often provides references to scientific studies and the Wikipedia article on Mindfulness is no exception.
The main section of the article has
...Studies have also shown that rumination and worry contribute to mental illnesses such as depression and anxiety, and that mindfulness-based interventions are effective in the reduction of both rumination and worry.
Mindfulness practice is being employed in psychology to alleviate a variety of mental and physical conditions, such as bringing about reductions in depression symptoms, reducing stress, anxiety, and in the treatment of drug addiction. Recent studies demonstrate that mindfulness meditation significantly attenuates pain through multiple, unique mechanisms. It has gained worldwide popularity as a distinctive method to handle emotions.
Clinical studies have documented both physical and mental health benefits of mindfulness in different patient categories as well as in healthy adults and children.
Research on the neural perspective of how mindfulness meditation works suggests that it exerts its effects in components of attention regulation, body awareness and emotional regulation. When considering aspects such as sense of responsibility, authenticity, compassion, self-acceptance and character, studies have shown that mindfulness meditation contributes to a more coherent and healthy sense of self and identity. Neuroimaging techniques suggest that mindfulness practices such as mindfulness meditation are associated with “changes in the anterior cingulate cortex, insula, temporo-parietal junction, fronto-limbic network and default mode network structures." Further, mindfulness-induced emotional and behavioral changes have been found to be related to functional and structural changes in the brain.
There is also a scientific research section
Mindfulness has gained increasing empirical attention ever since 1970.[unreliable source?] According to a 2015 systematic review and meta-analysis of systematic reviews of RCTs, evidence supports the use of mindfulness programs to alleviate symptoms of a variety of mental and physical disorders. Other reviews report similar findings. Further, mindfulness meditation appears to bring about favorable structural changes in the brain, and may also prevent or delay the onset of mild cognitive impairment and Alzheimer's disease. Mindfulness proved to be effective also in enhancing people’s capacity to self-regulate.
These are provided in the full article
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plus, there are so many referenced studies and articles of scientific research connected to this (I counted 25 in total - 156 in the full article) that providing a full list of references here would take me an age to provide in full (with weblinks etc.) on this site.